Question

In triunghiul ABC, masura unghiului A = 90⁰
AB= 4cm
BC=12cm
AD⊥ BC

AC=?
AD=?
Aria triunghiului ABC = ?

Answer 1

$AB^2+AC^2=BC^2 \\ \\ AC^2=12^2+4^2 \\ \\ AC^2=144-16 \\ \\ AC^2=128 \\ \\ AC=\sqrt{128}=8\sqrt{2}$

Teorema catetei
$AB^2=BD\cdot BC \\ \\ 4^2=12BD \\ \\ 12BD=16 \\ \\ BD=\frac{4}{3} \\ \\ DC=12-\frac{4}{3}=\frac{32}{3}~cm[tex] Teorema inaltimii [tex]AD^2=BD^2+DC^2=\frac{16}{9}+\frac{1024}{9}=\frac{1040}{9} \\ \\ AD=\frac{\sqrt{1040}}{3}=\frac{4\sqrt{65}}{3}$